Search NASA⌕ Search

SEARCH · Search NASA

Results for “Scale Invariance”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,027 records · Page 57

Double-Helical Tiled Chain Structure of the Twist-Bend Liquid Crystal Phase in CB7CB

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πR mol , where R mol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain.

36 MATERIALS SCIENCE↗

Electric field variations during substorms: OGO-6 measurements

The OGO-6 electric field measurements make it clear that the general pattern of high latitude electric fields in magnetic time-invariant latitude coordinates is not highly variable and that when unusual variations, or field distributions, occur they are relatively isolated in time and spatial extent. Thus, electric field changes on a global scale cannot, in general, be evoked as a direct cause of substorms. Polar traverses along the 18(h) to 6(h) magnetic time meridian show that the sum of potential drops across the evening auroral belt and morning auroral belt approximately equals the potential drop across the polar cap. The integrated polar cap potential drop ranges from 20 to 100 keV and values in the center of this range are most common under conditions of moderate magnetic disturbance. Roughly near 18(h) magnetic local time, a latitudinally narrow strip at the transition between auroral belt and polar cap fields exhibits unusually large field fluctuations immediately following the sudden onset of a negative bay at later magnetic local times. It appears likely that this spatially isolated correlation is related to an effect rather than a cause of substorm enhancement.

Heppner, J. P.↗

Solar flux forecasting using mutual information with an optimal delay

Solar flux F(sub 10.7) directly affects the atmospheric density, thereby changing the lifetime and prediction of satellite orbits. For this reason, accurate forecasting of F(sub 10.7) is crucial for orbit determination of spacecraft. Our attempts to model and forecast F(sub 10.7) uncovered highly entangled dynamics. We concluded that the general lack of predictability in solar activity arises from its nonlinear nature. Nonlinear dynamics allow us to predict F(sub 10.7) more accurately than is possible using stochastic methods for time scales shorter than a characteristic horizon, and with about the same accuracy as using stochastic techniques when the forecasted data exceed this horizon. The forecast horizon is a function of two dynamical invariants: the attractor dimension and the Lyapunov exponent. In recent years, estimation of the attractor dimension reconstructed from a time series has become an important tool in data analysis. In calculating the invariants of the system, the first necessary step is the reconstruction of the attractor for the system from the time-delayed values of the time series. The choice of the time delay is critical for this reconstruction. For an infinite amount of noise-free data, the time delay can, in principle, be chosen almost arbitrarily. However, the quality of the phase portraits produced using the time-delay technique is determined by the value chosen for the delay time. Fraser and Swinney have shown that a good choice for this time delay is the one suggested by Shaw, which uses the first local minimum of the mutual information rather than the autocorrelation function to determine the time delay. This paper presents a refinement of this criterion and applies the refined technique to solar flux data to produce a forecast of the solar activity.

Ashrafi, S.↗

Consistency relations for the conformal mechanism

We systematically derive the consistency relations associated to the non-linearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearly-realized de Sitter subalgebra. These identities relate (N+1)-point correlation functions with a soft external Goldstone to N-point functions. These relations have direct implications for the recently proposed conformal mechanism for generating density perturbations in the early universe. We study the observational consequences, in particular a novel one-loop contribution to the four-point function, relevant for the stochastic scale-dependent bias and CMB μ-distortion.

79 ASTRONOMY AND ASTROPHYSICS↗

Inflationary power asymmetry from primordial domain walls

We study the asymmetric primordial fluctuations in a model of inflation in which translational invariance is broken by a domain wall. We calculate the corrections to the power spectrum of curvature perturbations; they are anisotropic and contain dipole, quadrupole, and higher multipoles with non-trivial scale-dependent amplitudes. Inspired by observations of these multipole asymmetries in terms of two-point correlations and variance in real space, we demonstrate that this model can explain the observed anomalous power asymmetry of the cosmic microwave background (CMB) sky, including its characteristic feature that the dipole dominates over higher multipoles. We test the viability of the model and place approximate constraints on its parameters by using observational values of dipole, quadrupole, and octopole amplitudes of the asymmetry measured by a local-variance estimator. We find that a configuration of the model in which the CMB sphere does not intersect the domain wall during inflation provides a good fit to the data. We further derive analytic expressions for the corrections to the CMB temperature covariance matrix, or angular power spectra, which can be used in future statistical analysis of the model in spherical harmonic space.

79 ASTRONOMY AND ASTROPHYSICS↗

A multiresolution wavelet representation in two or more dimensions

In the multiresolution approximation, a signal is examined on a hierarchy of resolution scales by projection onto sets of smoothing functions. Wavelets are used to carry the detail information connecting adjacent sets in the resolution hierarchy. An algorithm has been implemented to perform a multiresolution decomposition in n greater than or equal to 2 dimensions based on wavelets generated from products of 1-D wavelets and smoothing functions. The functions are chosen so that an n-D wavelet may be associated with a single resolution scale and orientation. The algorithm enables complete reconstruction of a high resolution signal from decomposition coefficients. The signal may be oversampled to accommodate non-orthogonal wavelet systems, or to provide approximate translational invariance in the decomposition arrays.

Bromley, B. C.↗

Design and Use of Microphone Directional Arrays for Aeroacoustic Measurements

An overview of the development of two microphone directional arrays for aeroacoustic testing is presented. These arrays were specifically developed to measure airframe noise in the NASA Langley Quiet Flow Facility. A large aperture directional array using 35 flush-mounted microphones was constructed to obtain high resolution noise localization maps around airframe models. This array possesses a maximum diagonal aperture size of 34 inches. A unique logarithmic spiral layout design was chosen for the targeted frequency range of 2-30 kHz. Complementing the large array is a small aperture directional array, constructed to obtain spectra and directivity information from regions on the model. This array, possessing 33 microphones with a maximum diagonal aperture size of 7.76 inches, is easily moved about the model in elevation and azimuth. Custom microphone shading algorithms have been developed to provide a frequency- and position-invariant sensing area from 10-40 kHz with an overall targeted frequency range for the array of 5-60 kHz. Both arrays are employed in acoustic measurements of a 6 percent of full scale airframe model consisting of a main element NACA 632-215 wing section with a 30 percent chord half-span flap. Representative data obtained from these measurements is presented, along with details of the array calibration and data post-processing procedures.

Humphreys, William M., Jr.↗

Wavespace-Based Coherent Deconvolution

Array deconvolution is commonly used in aeroacoustic analysis to remove the influence of a microphone array's point spread function from a conventional beamforming map. Unfortunately, the majority of deconvolution algorithms assume that the acoustic sources in a measurement are incoherent, which can be problematic for some aeroacoustic phenomena with coherent, spatially-distributed characteristics. While several algorithms have been proposed to handle coherent sources, some are computationally intractable for many problems while others require restrictive assumptions about the source field. Newer generalized inverse techniques hold promise, but are still under investigation for general use. An alternate coherent deconvolution method is proposed based on a wavespace transformation of the array data. Wavespace analysis offers advantages over curved-wave array processing, such as providing an explicit shift-invariance in the convolution of the array sampling function with the acoustic wave field. However, usage of the wavespace transformation assumes the acoustic wave field is accurately approximated as a superposition of plane wave fields, regardless of true wavefront curvature. The wavespace technique leverages Fourier transforms to quickly evaluate a shift-invariant convolution. The method is derived for and applied to ideal incoherent and coherent plane wave fields to demonstrate its ability to determine magnitude and relative phase of multiple coherent sources. Multi-scale processing is explored as a means of accelerating solution convergence. A case with a spherical wave front is evaluated. Finally, a trailing edge noise experiment case is considered. Results show the method successfully deconvolves incoherent, partially-coherent, and coherent plane wave fields to a degree necessary for quantitative evaluation. Curved wave front cases warrant further investigation. A potential extension to nearfield beamforming is proposed.

Bahr, Christopher J.↗

Risk Assessment and Monitoring of Stored CO2 in Organic Rocks Under Non-Equilibrium Conditions

The USA is embarking upon tackling the serious environmental challenges posed to the world by greenhouse gases, especially carbon dioxide (CO2). The dimension of the problem is daunting. In fact, according to the Energy Information Agency, nearly 6 billion metric tons of CO2 were produced in the USA in 2007 with coal-burning power plants contributing about 2 billion metric tons. To mitigate the concerns associated with CO2 emission, geological sequestration holds promise. Among the potential geological storage sites, unmineable coal seams and shale formations in particular show promise because of the probability of methane recovery while sequestering the CO2. However. the success of large-scale sequestration of CO2 in coal and shale would hinge on a thorough understanding of CO2's interactions with host reservoirs. An important parameter for successful storage of CO2 reservoirs would be whether the pressurized CO2 would remain invariant in coal and shale formations under reasonable internal and/or external perturbations. Recent research has brought to the fore the potential of induced seismicity, which may result in caprock compromise. Therefore, to evaluate the potential risks involved in sequestering CO2 in Illinois bituminous coal seams and shale, we studied: (i) the mechanical behavior of Murphysboro (Illinois) and Houchin Creek (Illinois) coals, (ii) thermodynamic behavior of Illinois bituminous coal at - 100oC ≤ T ≤ 300oC, (iii) how high pressure CO2 (up to 20.7 MPa) modifies the viscosity of the host, (iv) the rate of emission of CO2 from Illinois bituminous coal and shale cores if the cores, which were pressurized with high pressure (≤ 20.7 MPa) CO2, were exposed to an atmospheric pressure, simulating the development of leakage pathways, (v) whether there are any fractions of CO2 stored in these hosts which are resistance to emission by simply exposing the cores to atmospheric pressure, and (vi) how compressive shockwaves applied to the coal and shale cores, which were pressurized with high pressure CO2, determine the fate of sequestered CO2 in these cores. Our results suggested that Illinois bituminous coal in its unperturbed state, i.e., when not pressurized with CO2, showed large variations in the mechanical properties. Modulus varied from 0.7 GPa to 3.4 GPa even though samples were extracted from a single large chunk of coal. We did not observe any glass transition for Illinois bituminous coal at - 100oC ≤ T ≤ 300oC, however, when the coal was pressurized with CO2 at ambient ≤ P ≤ 20.7 MPa, the viscosity of the coal decreased and inversely scaled with the CO2 pressure. The decrease in viscosity as a function of pressure could pose CO2 injection problems for coal as lower viscosity would allow the solid coal to flow to plug the fractures, fissures, and cleats. Our experiments also showed a very small fraction of CO2 was absorbed in coal; and when CO2 pressurized coals were exposed to atmospheric conditions, the loss of CO2 from coals was massive. Half of the sequestered gas from the coal cores was lost in less than 20 minutes. Our shockwave experiments on Illinois bituminous coal, New Albany shale (Illinois), Devonian shale (Ohio), and Utica shale (Ohio) presented clear evidence that the significant emission of the sequestered CO2 from these formations cannot be discounted during seismic activity, especially if caprock is compromised. It is argued that additional shockwave studies, both compressive and transverse, would be required for successfully mapping the risks associated with sequestering high pressure CO2 in coal and shale formations.

Malhotra, Vivak↗

Conformal consistency relations for single-field inflation

We generalize the single-field consistency relations to capture not only the leading term in the squeezed limit — going as 1/q{sup 3}, where q is the small wavevector — but also the subleading one, going as 1/q{sup 2}. This term, for an (n+1)-point function, is fixed in terms of the variation of the n-point function under a special conformal transformation; this parallels the fact that the 1/q{sup 3} term is related with the scale dependence of the n-point function. For the squeezed limit of the 3-point function, this conformal consistency relation implies that there are no terms going as 1/q{sup 2}. We verify that the squeezed limit of the 4-point function is related to the conformal variation of the 3-point function both in the case of canonical slow-roll inflation and in models with reduced speed of sound. In the second case the conformal consistency conditions capture, at the level of observables, the relation among operators induced by the non-linear realization of Lorentz invariance in the Lagrangian. These results mean that, in any single-field model, primordial correlation functions of ζ are endowed with an SO(4,1) symmetry, with dilations and special conformal transformations non-linearly realized by ζ. We also verify the conformal consistency relations for any n-point function in models with a modulation of the inflaton potential, where the scale dependence is not negligible. Finally, we generalize (some of) the consistency relations involving tensors and soft internal momenta.

79 ASTRONOMY AND ASTROPHYSICS↗

Generalised tensor fluctuations and inflation

Using an effective field theory approach to inflation, we examine novel properties of the spectrum of inflationary tensor fluctuations, that arise when breaking some of the symmetries or requirements usually imposed on the dynamics of perturbations. During single-clock inflation, time-reparameterization invariance is broken by a time-dependent cosmological background. In order to explore more general scenarios, we consider the possibility that spatial diffeomorphism invariance is also broken by effective mass terms or by derivative operators for the metric fluctuations in the Lagrangian. We investigate the cosmological consequences of the breaking of spatial diffeomorphisms, focussing on operators that affect the power spectrum of fluctuations. We identify the operators for tensor fluctuations that can provide a blue spectrum without violating the null energy condition, and operators for scalar fluctuations that lead to non-conservation of the comoving curvature perturbation on superhorizon scales even in single-clock inflation. In the last part of our work, we also examine the consequences of operators containing more than two spatial derivatives, discussing how they affect the sound speed of tensor fluctuations, and showing that they can mimic some of the interesting effects of symmetry breaking operators, even in scenarios that preserve spatial diffeomorphism invariance.

79 ASTRONOMY AND ASTROPHYSICS↗

Small-Scale Dissipation in Binary-Species Transitional Mixing Layers

Motivated by large eddy simulation (LES) modeling of supercritical turbulent flows, transitional states of databases obtained from direct numerical simulations (DNS) of binary-species supercritical temporal mixing layers were examined to understand the subgrid-scale dissipation, and its variation with filter size. Examination of the DSN-scale domain- averaged dissipation confirms previous findings that, out of the three modes of viscous, temperature and species-mass dissipation, the species-mass dissipation is the main contributor to the total dissipation. The results revealed that the percentage of species-mass by total dissipation is nearly invariant across species systems and initial conditions. This dominance of the species-mass dissipation is due to high-density-gradient magnitude (HDGM) regions populating the flow under the supercritical conditions of the simulations; such regions have also been observed in fully turbulent supercritical flows. The domain average being the result of both the local values and the extent of the HDGM regions, the expectations were that the response to filtering would vary with these flow characteristics. All filtering here is performed in the dissipation range of the Kolmogorov spectrum, at filter sizes from 4 to 16 times the DNS grid spacing. The small-scale (subgrid scale, SGS) dissipation was found by subtracting the filtered-field dissipation from the DNS-field dissipation. In contrast to the DNS dissipation, the SGS dissipation is not necessarily positive; negative values indicate backscatter. Backscatter was shown to be spatially widespread in all modes of dissipation and in the total dissipation (25 to 60 percent of the domain). The maximum magnitude of the negative subgrid- scale dissipation was as much as 17 percent of the maximum positive subgrid- scale dissipation, indicating that, not only is backscatter spatially widespread in these flows, but it is considerable in magnitude and cannot be ignored for the purposes of LES modeling. The Smagorinsky model, for example, is unsuited for modeling SGS fluxes in the LES because it cannot render backscatter. With increased filter size, there is only a modest decrease in the spatial extent of backscatter. The implication is that even at large LES grid spacing, the issue of backscatter and related SGS-flux modeling decisions are unavoidable. As a fraction of the total dissipation, the small-scale dissipation is between 10 and 30 percent of the total dissipation for a filter size that is four times the DNS grid spacing, with all OH cases bunched at 10 percent, and the HN cases spanning 24 30 percent. A scale similarity was found in that the domain-average proportion of each small-scale dissipation mode, with respect to the total small-scale dissipation, is very similar to equivalent results at the DNS scale. With increasing filter size, the proportion of the small-scale dissipation in the dissipation increases substantially, although not quite proportionally. When the filter size increases by four-fold, 52 percent for all OH runs, and 70 percent for HN runs, of the dissipation is contained in the subgrid-scale portion with virtually no dependence on the initial conditions of the DNS. The indications from the dissipation analysis are that modeling efforts in LES of thermodynamically supercritical flows should be focused primarily on mass-flux effects, with temperature and viscous effects being secondary. The analysis also reveals a physical justification for scale-similarity type models, although the suitability of these will need to be confirmed in a posteriori studies.

Bellan, Josette↗

Thermal axion production in the primordial quark-gluon plasma

We calculate the rate for thermal production of axions via scattering of quarks and gluons in the primordial quark-gluon plasma. To obtain a finite result in a gauge-invariant way that is consistent to leading order in the strong gauge coupling, we use systematic field theoretical methods such as hard thermal loop resummation and the Braaten-Yuan prescription. The thermally produced yield, the decoupling temperature, and the density parameter are computed for axions with a mass below 10 meV. In this regime, with a Peccei-Quinn scale above 6x10{sup 8} GeV, the associated axion population can still be relativistic today and can coexist with the axion cold dark matter condensate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Analytic, non-perturbative, gauge-invariant quantum chromodynamics: Nucleon scattering and binding potentials

Removal of the quenched approximation in the mechanism which produced an analytic estimate of quark-binding potentials, along with a reasonable conjecture of the color structure of the nucleon formed by such a binding potential, is shown to generate an effective nucleon scattering and binding potential. The mass-scale factor on the order of the pion mass, previously introduced to define the transverse imprecision of quark coordinates, is again used, while the strength of the potential is proportional to the square of a renormalized quantum chromodynamics (QCD) coupling constant. The potential so derived does not include corrections due to spin, angular momentum, nucleon structure, and electroweak interactions; rather, it is qualitative in nature, showing how Nuclear Physics can arise from fundamental QCD. -- Highlights: •Nucleon–nucleon forces are derived qualitatively from basic realistic quantum chromodynamics. •An effective nucleon binding is obtained from the simplest unquenched approximation. •A model deuteron binding energy of −2.2 MeV follows with α{sub s,R}=12.5.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Models of Earth's Atmosphere (120 to 1000 Km)

Atmospheric conditions encountered by a spacecraft in orbit about the Earth are important factors in space vehicle design, mission planning, and mission operations. Density is the primary atmospheric property that affects the spacecraft's orbital altitude, lifetime, and motion in the altitude range of 120 to 1000 kilometers. Near the lower limit of this range where density is greatest, a spacecraft will generally remain in orbit for a very short time; near the upper limit, the density effect on orbital lifetime is almost negligible. Density directly affects the torques which result from aerodynamic interaction between the space vehicle and the atmosphere; such torques must be considered in design of spacecraft attitude control systems. Density scale height is required in heating calculations for space vehicles re-entering the Earth's upper atmosphere. Density as well as chemical composition and temperature are needed in calculating a spacecraft's drag coefficient. Chemical composition and temperature also are required in the design of experiment sensors to be flown in this altitude range. Because of variability of atmospheric conditions with spatial location and solar condition, invariant models of the Earth's atmosphere (120 to 1000 kilometers) would not be useful for most engineering applications. Therefore, this monograph presents a computerized version of Jacchia's prediction method to provide models of the Earth's atmosphere which vary with solar condition and location. The resulting atmospheric models, which are predicted for particular times and locations, provide atmospheric density, chemical composition, temperature, molecular mass, and density scale height between 120 and 1000 kilometers altitude. In addition to the computerized method, a quick-look prediction method is given that may be used to obtain an estimate of atmospheric density for any time and spatial location without the use of a computer. A sample problem illustrates this method. Both methods provide models of mean density and models having reasonable upper extremes for density. The analytical approaches in both methods are considered to be the best available, but they could be refined considerably by additional data and study. Information contained in this monograph applies to altitudes between 120 and 1000 kilometers; other design criteria monographs in this series will provide atmospheric information below this altitude region.

Weidner, D. K.↗

Influence of Soil Moisture on the Development of Organized Convective Systems in South America

Abstract This study investigates the role of soil moisture (SM) on the initiation and organization of convective systems using the convection‐permitting ICOsahedral Non‐hydrostatic (ICON) model. We conduct two sets of experiments: a Control experiment with interactive SM and a fixed SM experiment (FixedSM) with invariable SM conditions. We focus on two regions in South America: the Amazon and southeastern South America (SESA). Larger organized convective systems are associated with greater SM heterogeneity in both regions, though other large‐scale synoptic influences affect the robustness of this relationship in SESA. These results remain largely unaffected by disabling the effects of precipitation on SM in the FixedSM experiment, and complementary analyses using satellite‐based estimates of SM and precipitation support these findings. Spatial compositing of mesoscale environments in the Amazon shows the presence of well‐defined SM gradients, at a length scale of a few hundred kilometers, many hours before convective system detection. Larger SM gradients correspond to larger gradients in thermodynamic variables, particularly surface temperature and sensible heat flux, and are associated with larger convective systems. Overall, our findings suggest that surface heterogeneities such as SM gradients not only affect deep convection initiation, as previously suggested, but they can also encourage the growth and organization of convective systems into larger clusters, particularly in the absence of significant synoptic influences.

54 ENVIRONMENTAL SCIENCES↗

MEASURING GRAVITATIONAL LENSING FLEXION IN A1689 USING AN ANALYTIC IMAGE MODEL

Measuring dark matter substructure within galaxy cluster halos is a fundamental probe of the {Lambda}CDM model of structure formation. Gravitational lensing is a technique for measuring the total mass distribution which is independent of the nature of the gravitating matter, making it a vital tool for studying these dark-matter-dominated objects. We present a new method for measuring weak gravitational lensing flexion fields, the gradients of the lensing shear field, to measure mass distributions on small angular scales. While previously published methods for measuring flexion focus on measuring derived properties of the lensed images, such as shapelet coefficients or surface brightness moments, our method instead fits a mass-sheet transformation invariant Analytic Image Model (AIM) to each galaxy image. This simple parametric model traces the distortion of lensed image isophotes and constrains the flexion fields. We test the AIM method using simulated data images with realistic noise and a variety of unlensed image properties, and show that it successfully reproduces the input flexion fields. We also apply the AIM method for flexion measurement to Hubble Space Telescope observations of A1689 and detect mass structure in the cluster using flexion measured with this method. We also estimate the scatter in the measured flexion fields due to the unlensed shape of the background galaxies and find values consistent with previous estimates.

79 ASTRONOMY AND ASTROPHYSICS↗

Infrared fixed point in SU(2) gauge theory with adjoint fermions

We apply Schroedinger-functional techniques to the SU(2) lattice gauge theory with N{sub f}=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g{sub *} where 1/g{sub *}{sup 2}=0.20(4)(3). At the fixed point, we find a mass anomalous dimension {gamma}{sub m}(g{sub *})=0.31(6).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗